Ground motion time histories are numerical descriptions of how a certain ground motion parameter, such as acceleration, varies with time. They provide a full description of the earthquake motion, unlike response spectra, as they show duration as well as amplitude and frequency content. They are usually expressed as plots of the ground motion parameter versus time, but consist of discrete parameter-time pairs of values. Idealized time histories are sometimes represented by simple mathematical functions such as sine waves, but real earthquake motions are far too complex to be represented mathematically. There are two general types of time histories:
Time histories are used in analysis rather than design. Various codes stipulate the minimum numbers of records to be used (typically, from 3 to 7) in analyses of irregular structures and buildings employing seismic isolation or energy dissipation systems. Dynamic analysis using time histories is often performed for important structures and is becoming more and more common as computer modeling and analysis capabilities advance.
Where site-specific ground motion records are available, they can be used to develop design response spectra. However, time histories are usually selected to "fit" a target response spectrum.
A response spectrum is a plot of the maximum responses of a number of single degree of freedom systems with different natural periods to the same input ground motion time history. Generalized, smoothed spectra, rather than the jagged spectra that result from a specific time history are used for design. These spectra are termed design response spectra or target response spectra, and are often used to select appropriate time histories. The two basic types of spectra, linear elastic and nonlinear inelastic, will be covered in detail in two sections, Elastic Response and Inelastic Response.